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• W1843670779 abstract "Isogenies are the morphisms between elliptic curves and are, accordingly, a topic of interest in the subject. As such, they have been well studied, and have been used in several cryptographic applications. Vélu’s formulas show how to explicitly evaluate an isogeny, given a specification of the kernel as a list of points. However, Vélu’s formulas only work for elliptic curves specified by a Weierstrass equation. This paper presents formulas similar to Vélu’s that can be used to evaluate isogenies on Edwards curves and Huff curves, which are normal forms of elliptic curves that provide an alternative to the traditional Weierstrass form. Our formulas are not simply compositions of Vélu’s formulas with mappings to and from Weierstrass form. Our alternate derivation yields efficient formulas for isogenies with lower algebraic complexity than such compositions. In fact, these formulas have lower algebraic complexity than Vélu’s formulas on Weierstrass curves." @default.
• W1843670779 created "2016-06-24" @default.
• W1843670779 creator A5022110332 @default.
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• W1843670779 date "2015-09-09" @default.
• W1843670779 modified "2023-10-13" @default.
• W1843670779 title "Analogues of Vélu’s formulas for isogenies on alternate models of elliptic curves" @default.
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• W1843670779 doi "https://doi.org/10.1090/mcom/3036" @default.
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